Definition
Mathematically, shape optimization can be posed as the problem of finding a bounded set, minimizing a functional
- ,
possibly subject to a constraint of the form
Usually we are interested in sets which are Lipschitz or C1 boundary and consist of finitely many components, which is a way of saying that we would like to find a rather pleasing shape as a solution, not some jumble of rough bits and pieces. Sometimes additional constraints need to be imposed to that end to ensure well-posedness of the problem and uniqueness of the solution.
Shape optimization is an infinite-dimensional optimization problem. Furthermore, the space of allowable shapes over which the optimization is performed does not admit a vector space structure, making application of traditional optimization methods more difficult.
Read more about this topic: Shape Optimization
Famous quotes containing the word definition:
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)